3-1

Chap. 5 (Signals and Noise), Chap. 6 (Spectroscopy introduction)

• Signal to noise • Source of noise• Signal to noise enhancement

• Signal has the information of the analyte• Noise is the extraneous information in the information due to electronics,

spurious response, and random events

• Signal to noise ratio Noise is generally constant and independent of the signal The impact of noise is greatest on the lowest signal

The ratio of signal to noise is useful in evaluating data

3-2

Signal to Noise• Value of the signal to

noise can vary Values less than 3

make it hard to detect signal

s

x

deviationdards

mean

N

S

tan

3-3

Sources of Noise

• Chemical Noise Uncontrollable variables affecting

chemistry of system under investigationChange in equilibria due to variations

* Temperature* Pressure* Sample variation* Humidity

3-4

Source of Noise

• Instrumental Noise Thermal noise Shot noise Flicker Environmental noise

• Thermal noise Thermal agitation of electrons in electronics

Boltzmann’s equation

3-5

Instrument Noise

• Based on Boltzmann R is resistance k is Boltzmann’s constant

1.38E-23 J/K T in K f is frequency bandwith (1/3*risetime)

Relates to response time in instrument

• Shot Noise Electrons crossing a junction

pn junction, anode and cathode Random events e = 1.6e-19 C

fkTRvrms 4

fIeirms 2

3-6

Instrument Noise• Flicker Noise

Inverse of signal frequency Important below 100 HzDrift in instruments

• Environmental Noise Emanates from surroundings

Electromagnetic radiation

3-7

Signal to Noise Enhancement

• Hardware and software methods Hardware is based on instrument design

Filters, choppers, shields, detectors, modulators

Software allows data manipulation

• Grounding and Shielding Absorb electromagnetic radiation

Prevent transmission to the equipment

* Protect circuit with conduction material and ground

Important for amplification

3-8

Hardware

• Difference and Instrumentation Amplifiers Subtraction of noise from a circuit

Controlled by a single resistorSecond stage subtracts noise

Used for low level signal• Analog filtering

Uses a filter circuit Restricts frequency

3-9

Hardware

• Modulation Changes low frequency signal to higher

frequencySignal amplified, filter with a high pass

filter, demodulation, low pass filter• Signal Chopping

Input signal converted to square wave by electronic or mechanical chopperSquare wave normalizes signal

3-10

Software Methods• Ensemble Average

Average of spectra Average can also

be sum of collected spectra

• Boxcar average Average of points

in a spectra

3-11

Software Methods

3-12

Digital Filtering

• Numerical methods Fourier transform

Time collected data converted to frequency

* NMR, IR Least squares smoothing

Similar to boxcar

* Uses polynomial for fit Correlation

3-13

Chap. 6 Introduction to Spectrometric Methods

• Electromagnetic radiation

• Interaction with matter• Quantum mechanical

properties

• Electromagnetic radiation orthogonal in phase

oscillations

3-14

Wave Parameters

• Amplitude and wavelength

3-15

Electromagnetic Spectrum

 

                                                  

                                                                                                                  

       

3-16

Methods

3-17

X-ray Structure

• X-rays0.01 to 100 angtroms

12 keV to 1 MeVIonizing radiation

• RoentgenGas discharge tubeDetector with Ba/Pt CN

Scintillator

3-18

• In November of 1895, Wilhelm Roentgen (1845 - 1923) was working in his laboratory using a Crookes tube (known in German as either a Hittorf valve or a Hittorf-Crookes tube) when he noticed that a sample of barium platinocyanide, which accidentally lay on the table, gave off a fluorescent glow. As the Crookes tube was covered at the time, Roentgen was puzzled as to the mechanism whereby the platinum compound was being stimulated to glow. After carrying out a series of exceptionally careful experiments, Roentgen realized that the Crookes tube was emitting a new kind of radiation which he described as "X-rays". In investigating the penetrating ability of these rays, Roentgen placed a photographic plate behind his wife's hand and recorded the first x-ray photo. In this figure, below, notice his wife's wedding rings that stand out as dark rings.

3-19

3-20

Energy from X-ray

• From Cu13.6(29^2)=11.4 keV

Based on Bohr atom

Family of lines due to different levels

• Determination of elements

3-21

3-22

Mosley

• Measured 38 elementsMeasured emission

spectra and found pattern

Based on Z, not mass (Ar/K, Co/Ni, Te/I)

Place lanthanides on periodic table14 lanthanides

Up to U there are 92 elements

3-23

3-24

3-25

X-ray Structure

• Review of cathode ray tube and nomenclature

• Determination of elements from X-rays

• Coolidge1913

Vacuum tube

* Reduction of collision with gas

* Reduce glowHeating CathodeWater coolingShielding (Pb), Be windows

3-26

X ray linesLines with continuum

function of voltage

Mo BCC

from bremstrallung

3-27

Bremsstrahlung

E=qV=eV=E(photon)=12400/V Ang

Duane-hunt law

3-28

Use x-ray to examine crystals

• Model atoms as mirrorsUse classical optics

• Utilize interferenceConstructive and destructive

3-29

X-ray diffraction

• Emission spectrum from x-ray generatorComposite of 2

spectraCharacteristic

spectraContinuous

spectraCalculate lines by

Mosley’s Law

3-30

Braggs Law

Specifics conditions for interference

Set of reflections identifies structure

3-31

XRD

• Fixed wavelength, vary angle

• Powder specimen

• Grains act as single crystal

• Plot I vs angleAt Bragg angle produce

angle

3-32

Data analysis

Normalize data to 1st sin^2theta

Clear fractions

Speculate on hkl

Know wavelength from source, solve for a

3-33

Laue Technique

3-34

Spot pattern

• For symmetry2, 3, 4 fold symmetry

• May not work for thick specimenBackscatter and transmission

3-35

Transmission of radiation• Polarization

Directional filtering of light Light will be scattered by larger molecules

• Radiation transfer to molecules Absorption spectroscopy

Material consideration* Glass, quartz, plastic

3-36

Atomic Spectra

• Quantum numbersn=1,2,3,4r=aon2/Z for gases with 1 electron

• EnergyE=-(mee4/8

2h2)Z2/n2

For ground state HE=2.18E-18 J/atom=k

* Can determine J/mole 1312 kJ/moleEnergy goes as –k/n2

* System converges to limit

3-37

Energy

• n=infinity, r=infinity , E=0, unbound e-

• Ionization energyk is ionization energy

• Velocityv=nh/2mer

• Ionization energyMinimum energy required to remove

electron from atom in gas phaseMultiple ionization energies

3-38

Balmer states

• Gas H in tubeFour lines in visible regionFit lines

• 1/=(1/22-1/n2)R, R=1.1E-7 m-1

1/(wavenumber)E=1/2mev2=eV (V=Volts)

At 1 V = 1.6E-19 J =eVK=13.6 eV

3-39

Matter energy interaction

• Eincident=1/2mv2=qV

• Escattered

E =Eincident-Escattered

E=kZ2(1/n2final-1/n2

in)=h=hc/

De-excitation of electron results in photon emissionCorresponds to line emission

3-40

Shell model and multielectrons

• Particle interactionParticle hits electron, electron has scatted kinetic

energyEinc=Ebinding+Eelectron scattered

* For ground state Ebinding is ionization energy

Einc= 0.5mv2

Etrans=-kZ2(1/n2)

For photon E=hc/

3-41

Rydberg)

n

1

n

1(

hc

k2o

2f

k/hc=1.1e-7 m-1 = R (Rydberg constant)

Visible light 400-700 nm (1.8 to 3.1 eV)

Quantum numbers

n=1,2,3,4

l=0 to n-1

ml= +-l

Spin=+-1/2

3-42

Bohr Atom

• Net force on the electron is zero0=Fdynamic+Fcoulombic

1/2mev2/r+q1q2/4r2

Force is 1/r2

Energy 1/r1/2mev2/r-Ze2/4r2

Z is charge on nucleus

• Quantize energy through angular momentummvr=nh/2n=1,2,3….

Can solve for r, E, v

FdrE

3-43

Bohr radius

• R=(h2/mee2)(n2/Z)

Radius is quantized and goes at n2

R=0.529 Å for Z=1, n=1Ao (Bohr radius)

3-44

Photoelectric effect